a dynamic paging scheme for long-term evolution mobility...

WIRELESS COMMUNICATIONS AND MOBILE COMPUTINGWirel. Commun. Mob. Comput. 2015; 15:629–638

Published online 2 April 2013 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/wcm.2371

RESEARCH ARTICLE

A dynamic paging scheme for long-term evolutionmobility managementYi-Bing Lin, Ren-Huang Liou* and Chun-Ting Chang

Department of Computer Science, National Chiao Tung University, Taiwan

ABSTRACT

In long-term evolution, the service area is partitioned into several tracking areas (TAs), which comprise one or more cells(the radio coverages of base stations). The TAs are grouped into TA list (TAL). When an incoming call arrives, the net-work attempts to connect to the user equipment (UE) by paging the cells in the UE’s TAL, which may incur large pagingtraffic that significantly consumes the limited radio resources. To resolve this issue, this paper proposes a dynamic pagingscheme that determines the paging sequence of cells in real time according to the UE movement and call behavior. Wecompare the performance of the dynamic paging with that of the previously proposed Cell-TA-TAL (CTT) paging. Ourstudy indicates that the dynamic paging outperforms the CTT paging when movement pattern is regular and the UE movesfrequently. Copyright © 2013 John Wiley & Sons, Ltd.

KEYWORDS

dynamic paging; long-term evolution (LTE); mobility management

*Correspondence

Ren-Huang Liou, Department of Computer Science, National Chiao Tung University, Taiwan.E-mail: [email protected]

1. INTRODUCTION

Mobility management of mobile telecom networks [1–4]tracks the user equipment (UE) through the location updateand the paging procedures. The location update proce-dure is executed when the UE moves from one location toanother location. When the network attempts to connect tothe UE (e.g., when an incoming call arrives), the networkexecutes the paging procedure by broadcasting the pag-ing messages to the base stations where the UE probablyresides.

In long-term evolution (LTE), the mobility managemententity (MME; Figure 1 (a)) is responsible for tracking thelocations of the UEs [5–7]. The MME is connected to agroup of base stations (evolved Node B). The radio cov-erages of the base stations are called cells (Figure 1 (b)).These cells are grouped into non-overlapped tracking areas(TAs) [5,6]. For example, in Figure 1 (c), TA 1 includesCells 1 and 2. Every TA has a unique TA identity (TAI).The TAs are further grouped into the TA lists (TALs). TheMME allocates the TAL to the UE via the location updateprocedure. For example, if the UE (Figure 1 (1)) updates itslocation in Cell 4, the MME allocates TAL 1 (Figure 1 (d))to the UE, where TAL 1D fTA 1;TA 2;TA 3g. Every basestation periodically broadcasts its TAI. The UE detects that

it has left the current TAL by searching the TAL for theTAI received from the the base station. If the receivedTAI is found in the TAL, it means that the UE does notleave the current TAL. Otherwise, the UE executes thelocation update procedure to inform the MME of its newlocation. Then, the MME allocates a new TAL to the UE.In Figure 1, when the UE moves from Cell 4 to Cell 7(Figure 1 (2)), the received TA 4 identity is not found inTAL 1. Therefore, the UE performs the location updateprocedure, and the MME allocates TAL 2 to the UE. Forthe TAL allocation, we consider the central policy [5] thatallocates the TAL whose central TA is the TA where the UEcurrently resides. In the central policy, the allocated TALsmay be overlapped. For example, in Figure 1, both TALs 1and 2 include TA 3.

When an incoming call arrives, the MME sends the pag-ing messages to the cells in the UE’s TAL to search theUE, which may incur large traffic that significantly con-sumes the limited radio resources. To resolve this issue, wepropose a dynamic paging scheme exercised at the MMEto reduce the paging traffic.

This paper is organized as follows. Section 2 proposesthe dynamic paging scheme. Section 3 describes a sim-ulation model for this scheme. Section 4 investigates theperformance of the dynamic paging scheme by numerical

Copyright © 2013 John Wiley & Sons, Ltd. 629

A dynamic paging scheme for LTE mobility management Y.-B. Lin, R.-H. Liou and C.-T. Chang

UE

UE

TA 1

TAL 11

2

c

d

MME

Cell 1

Cell 2

Cell 3

Cell 4

Cell 5

Cell 6

Cell 7

Cell 8

Cell 9

Cell 10

TA 2

TA 3

TA 4

TA 5

TAL 2

b

a

Figure 1. Long-term evolution mobility managementarchitecture.

Table I. The acronym list.

3G Third-generationCTT Cell-TA-TALLTE Long-term evolutionMME Mobility management entityTA Tracking areaTAI Tracking area identityTAL Tracking area listTT TA-TALUE User equipment

examples, and the conclusions are given in Section 5. Theacronyms used in the paper are listed in Table I.

2. DYNAMIC PAGING SCHEME

On the basis of the TA/TAL architecture described inSection 1, we have considered three paging schemes forLTE mobility management in [8]. The details are re-iterated here for the reader’s benefit. In these schemes,an interacted cell refers to a cell where the UE has inter-acted with the network (e.g., receives a call or performs alocation update).

Scheme Cell-TA-TAL (CTT). When an incoming call arrives,the MME first sends the paging message to the lastinteracted cell to alert the UE. If the MME doesnot receive the response within a timeout period, theMME sends the paging messages to the TA of the lastinteracted cell. If the MME still receives no response

from the UE, the MME sends the paging messages toall cells in the TAL.

Scheme TA-TAL (TT). When an incoming call arrives, theMME sends the paging messages to the TA of thelast interacted cell. If the MME does not receivethe response within a timeout period, the MME sendsthe paging messages to all cells in the TAL.

Scheme 3G (traditional third-generation approach). Whenan incoming call arrives, the MME sends the pagingmessages to all cells in the TAL simultaneously. Thisscheme is used in the existing 3G mobile networks [1].

We define a polling cycle [9] as the period between whenthe MME sends a paging message to alert the UE and whenthe MME receives the paging response or a timeout occurs.Let Np be the maximum number of polling cycles beforethe UE is found. The numbers Np of the CTT, the TT, andthe 3G schemes are 3, 2, and 1, respectively.

In [8], the performance of the three schemes was evalu-ated. The study indicated that depending on the UE move-ment patterns and call activities, one paging scheme mayoutperform the other two. This paper proposes a dynamicpaging scheme that automatically selects the ‘best’ pagingscheme in real time according to the UE movement and callbehavior.

Ideally, the dynamic paging selects the paging schemewith the smallest number of paged cells. Practically, theselection decision for a UE is made on the basis of theUE’s recent ‘behavior history’. Specifically, for the UE,the MME computes the average number of paged cells forthe CTT, TT, and 3G schemes in the m most recent incom-ing call arrivals. When the i th incoming call arrives, wedefine Cp;s.i/ as the average number of paged cells forthe s scheme in the m� D minfi � 1;mg most recent callarrivals, where s 2 fCT T ; T T ; 3Gg. When i D 1, wedo not have any history datum, and Cp;s.1/ D 0 for alls 2 fCT T ; T T ; 3Gg. To compute Cp;s.i/ with i � 2,we first introduce three scenarios when an incoming callarrives. In this paper, we denote NC and NT as the num-ber of cells in a TA and the number of TAs in a TAL,respectively.

Scenario 1. The UE resides in the last interacted cell. Inthis scenario, the number of cells that page the UE forCTT, TT, and 3G schemes are 1;NC , and NCNT ,respectively. In Figure 1, suppose that the last inter-acted cell is Cell 4. In this scenario, Cell 4 will pagethe UE for CTT. On the other hand, Cells 3 and 4 (TA2) will page the UE for TT, and Cells 1-6 (TAL 1)will page the UE for 3G.

Scenario 2. The UE resides in the TA of the last interactedcell but is not in the last interacted cell. In this sce-nario, the number of cells that page the UE for CTT,TT, and 3G schemes are 1CNC ; NC , and NCNT ,respectively. In Figure 1, suppose that the last inter-acted cell is Cell 4. For CTT paging, Cell 4 will pagethe UE, and then Cells 3 and 4 (TA 2) will page theUE. For TT paging, Cells 3 and 4 (TA 2) will page

630 Wirel. Commun. Mob. Comput. 2015; 15:629–638 © 2013 John Wiley & Sons, Ltd.DOI: 10.1002/wcm

Y.-B. Lin, R.-H. Liou and C.-T. Chang A dynamic paging scheme for LTE mobility management

the UE. For 3G paging, Cells 1-6 (TAL 1) will pagethe UE.

Scenario 3. The UE resides in the TAL but is not in the TAof the last interacted cell. In this scenario, the num-ber of cells that page the UE for CTT, TT, and 3Gschemes are 1C NC C NCNT ; NC C NCNT andNCNT , respectively. In Figure 1, suppose that thelast interacted cell is Cell 4. For CTT paging, Cell 4will page the UE, then Cells 3 and 4 (TA 2) will pagethe UE, and finally Cells 1–6 (TAL 1) will page theUE. For TT paging, Cells 3 and 4 (TA 2) will pagethe UE, and then Cells 1–6 (TAL 1) will page the UE.For 3G paging, Cells 1–6 (TAL 1) will page the UE.

In our approach, the MME records the scenario type ofeach call arrival. Let nI .i/ be the number of scenarios Ithat occurred between the .i � m�/th call arrival and the.i � 1/th call arrival where I 2 f1; 2; 3g. On the basis ofnI .i/, NC , and NT , Cp;s.i/ is computed as

Cp;CT T .i/D

8̂<̂ˆ̂:

n1.i/

m�C

�n3.i/

m�

�.NCNT C 1/; for NC D 1

n1.i/

m�C

�n2.i/

m�

�.1CNC /C

�n3.i/

m�

�.1CNC CNCNT /; for NC ¤ 1

(1)

Cp;T T .i/D

�n1.i/C n2.i/

m�

�NC

C

�n3.i/

m�

�.NC CNCNT /

(2)

and

Cp;3G.i/DNCNT (3)

In (1), for NC D 1 (i.e., the TA only contains one cell,and scenario 2 never occurs), if the UE is not found inthe last interacted cell, all cells in the TAL will page theUE for the CTT paging. Therefore, for the CTT pagingwith NC D 1, the number of cells that page the UE inscenario 3 is NCNT C 1. For CTT with NC ¤ 1, thenumbers of cells that page the UE are 1, 1 C NC , and1 C NC C NCNT for scenarios 1, 2, and 3, respectively(as previously mentioned). In (1)–(3), nI .i/ is affected bythe movement patterns and call activities of a user. Whenthe i th incoming call arrives, the MME selects the pagingscheme with the smallest Cp;s.i/ among the CTT, TT, and3G schemes. We note that if two or more schemes havethe smallest Cp;s.i/, the MME selects the one with thesmallest Np to reduce the paging delay.

3. SIMULATION MODEL

This section proposes a discrete-event simulation model(Monte Carlo simulation) to study the performance of thedynamic paging scheme. Note that our previous work indi-cated that the CTT scheme outperforms both the TT and

the 3G schemes with most input parameter setups [8].Therefore, it suffices to compare the performance of thedynamic paging scheme with that of the CTT scheme. Forthe dynamic paging (denoted as s DD) and the CTT pag-ing (denoted as s D CT T ), we consider two performancemeasures as follows:

� Cd;s : the expected number of polling cycles beforethe UE is found.

� Cp;s : the expected number of paged cells when anincoming call arrives.

It is clear that the smaller the aforementioned performancemeasures, the better the paging scheme.

For the demonstration purpose, we consider a two-dimensional (2D) mesh cell configuration (i.e., Manhattan-street-like layout) [10–15]. Figure 2 illustrates the meshcell configuration, where a cycle represents a cell, andeach cell has eight neighboring cells. Various movement

patterns can be investigated in our study. To highlight theeffect of ‘movement locality’, we considered the scenariowhere a UE moves to one direction with a probabilitydifferent from other directions [15]. In this paper, weextend the previous work by considering the followingmovement pattern: The UE moves to one of the upper-right, the right, and the lower-right neighboring cells withthe routing probability p and moves to one of the otherneighboring cells with the probability .1 � 3p/=5. It isclear that the movement pattern has the best locality whenp D 0:125.

On the basis of the mesh cell configuration, Figure 3shows a TAL configuration, where NC D NT D 9. In theTAL, the cells are labeled as hx; yi, where x is the columnlabel, y is the row label, and 1 � x; y �

pNCNT . The

1 - 3p

5

1 - 3p

5

1 - 3p

5

1 - 3p

5

1 - 3p

5

p

p

p

Figure 2. Mesh cell configuration and the movement directions.

Wirel. Commun. Mob. Comput. 2015; 15:629–638 © 2013 John Wiley & Sons, Ltd. 631DOI: 10.1002/wcm


1,9 2,9 3,9

1,8 2,8 3,8

1,7 2,7 3,7

TA 1,36,95,94,9

6,85,84,8

6,75,74,7

TA 2,39,98,97,9

9,88,87,8

9,78,77,7

TA 3,3

1,6 2,6 3,6

1,5 2,5 3,5

1,4 2,4 3,4

TA 1,26,65,64,6

6,55,54,5

6,45,44,4

TA 2,29,68,67,6

9,58,57,5

9,48,47,4

TA 3,2

1,3 2,3 3,3

3,22,21,2

3,12,11,1

TA 1,15,24,2

6,35,34,3

6,2

6,15,14,1

TA 2,19,38,37,3

9,28,27,2

9,18,17,1

TA 3,1

Figure 3. An example of the tracking area (TA) list configuration.NC D NT D 9/.

TAs are labeled as hX; Y i, where 1 � X; Y �pNT . TA

hX; Y i consists of cells hx; yi where .X � 1/pNC C 1 �

x �XpNC and .Y �1/

pNCC1� y � Y

pNC . To sim-

plify the discussions on the central policy, we assume thatpNT is an odd number. Because the central policy is exer-

cised, when the UE leaves the current TAL, the entranceTA is reset to the central TA of the ‘next’ TAL, and theentrance cell is reset to the cell in the central TA at the samerelative position. For example, in Figure 3, when the UE inCell h9; 1i moves to the right-hand side neighboring cell,the entrance cell is reset to Cell h4; 4i. In the simulation,an event e has two attributes as follows:

� The type attribute indicates one of the two eventtypes. A Call event represents a call arrival. When theCall event occurs, the MME searches the UE throughthe paging procedure. A Move event represents thatthe UE crosses the cell boundary to a neighboring cell.

� The ts attribute indicates the timestamp when theevent occurs.

The inter-call arrival time tc is a random number drawnfrom an exponential generator GC with the mean 1=�c .The residence time tm that the UE stays in a cell is a ran-dom number drawn from a Gamma generatorGM with themean 1=�m and the variance V . We consider the Gammadistribution because this distribution is widely used in tele-com modeling [8,9,15–18]. Other distributions such asWeibull and truncated Normal show similar results and willnot be presented here. Let U be a uniform random num-ber between 0 and 1 drawn from a generator GD . In thissimulation, the last interacted cell is labeled as h Nx; Nyi, andthe cell where the UE currently resides is represented byhx�; y�i. Three counters are used to measure the outputstatistics as follows:

� i : the number of incoming calls.� nd : the number of polling cycles.� np : the number of paged cells.

From the aforementioned counters, we compute

Cd;s Dnd

iand Cp;s D

np

i(4)

The details of the simulation procedure are given inAppendix A.

We validate the simulation model of the dynamic pag-ing by two analytic models as follows. Our previous work[8] proposed the analytic models to derive the paging costsof the CTT and TT schemes for the one-dimensional (1D)TAL configuration. The validation procedure is describedwith the following steps:

Step 1.1. For some input parameter setups (e.g., �m=�c D0:01, V D 1=�2m, NC D 3, NT D 15, p D 0:5,and m D 50), the dynamic paging will select theCTT scheme to search the UE in most incomingcalls (more than 99%). In this case, we comparethe paging cost of the dynamic paging with that ofthe CTT scheme derived in [8]. Our study indicatesthat the analytic and simulation results are consistent(the discrepancies are within 1%), and the details areomitted.

Step 1.2. Similar to Step 1.1, when �m=�c D 10, V D1=�2m, NC D 3, NT D 15, p D 0:9, and m D 50,the dynamic paging will select the TT scheme inmost incoming calls. Our study also shows that theanalytic and simulation results are consistent (thediscrepancies are within 1%).

Step 1.3. For other input parameter setups, the dynamicpaging may not always select the same pagingscheme. We modify the simulation program to recordthe percentages of calls where the CTT, TT, and 3Gschemes are exercised. From the percentages and thepaging costs derived in [8], we compute the expectedpaging cost of the dynamic paging scheme and com-pare the expected paging cost with the simulationresults. Our study indicates that the discrepancies arewithin 1%, and the analytic analysis is consistent withthe simulation results.

4. NUMERICAL EXAMPLES

This section compares the performance of the dynamicpaging scheme and the CTT paging scheme by numericalexamples. We consider the TAL’s size NCNT D 15

2. Forother NCNT values, the results are similar and are omit-ted. Our simulation experiments also show that m � 10

is appropriate. In this paper, we consider m D 20 andNC D 3

2.



4.1. Analysis of the Cd;s performance

This subsection investigates the effects of p, �m=�c , andV on the expected number Cd;s of polling cycles beforethe UE is found.

Effects of p: When p increases, the UE tends to moveto the right-hand side neighboring cells, and worselocality is expected. In this case, the UE is more likelyto be far away from the last interacted cell. There-fore, bothCd;D andCd;CT T increase as p increases.Figure 4 (a) shows that Cd;D=Cd;CT T increases asp increases, and the effect of p becomes more signif-icant when �m=�c increases (to be discussed next).

Clearly, the more the locality, the more the dynamicscheme outperforms the CTT scheme.

Effects of �m=�c: When �m=�c increases (i.e., morecell crossings during tc), the UE may be far awayfrom the last interacted cells, and higher Cd;D andCd;CT T are expected. Figure 4 (b) indicates thatCd;D=Cd;CT T decreases as �m=�c increases. Thisphenomenon is explained as follows. When �m=�cincreases, the dynamic paging is more likely to selectthe TT or the 3G scheme because the UE may be faraway from the last interacted cell. Because the pag-ing delays of the TT and 3G schemes are smaller thanthat of the CTT scheme, Cd;D=Cd;CT T decreases as�m=�c increases. The figure shows that the dynamic

Figure 4. Effects of p and �m=�c on Cd;D=Cd;CTT .NC D 32, NT D 52, mD 20, and V D 1=�2m/.

Figure 5. Effects of V and p on Cd;D=Cd;CTT (NC D 32, NT D 52, and mD 20).



Figure 6. Effects of �m=�c , p, and V on Cp;D=Cp;CTT (NC D 32, NT D 52, and mD 20).

scheme outperforms the CTT scheme in the �m=�crange being considered. We have also considered thescenario where �m=�c changes from time to time,and similar results are observed, which will not bepresented here.

Effects of V : When V is small (i.e., movement pattern isregular), most tm values are close to 1=�m. In thiscase, if �m=�c is small, the UE is more likely to befound in the last interacted cell, and the dynamic andCTT schemes have similar (and good) Cd;s perfor-mance (in Figure 5, for V � 1=�2m, the values of theı and � curves are close to 1). On the other hand,when �m=�c is large, dynamic paging outperformsCTT paging because the dynamic paging scheme ismore likely to select the TT or the 3G scheme, whichhas smaller paging delay (in Figure 5, for V � 1=�2m,the values of the ˘ curves are smaller than 1). For any�m value, when V increases, more longer tm periodsare observed, and the UE does not move in many con-secutive tc periods that fall in these tm. In this case,the UE is always found in the last interacted cell, andboth the dynamic paging and the CTT paging havesimilar performance (in Figures 5, for V > 102=�2m,the values of all curves are close to 1).

4.2. Analysis of the Cp;s performance

This subsection investigates the expected number Cp;s ofpaged cells when an incoming call arrives. The effects of�m=�c , p, and V on Cp;s are similar to those on Cd;sdescribed in Subsection 4.1. However the ‘degrees’ of theeffects of these parameters on Cp;s and Cd;s for the CTTand the dynamic schemes are different. A nontrivial resultis that Cp;D=Cp;CT T � 1 for various �m=�c , p, and Vvalues (as illustrated in Figure 6). The reason is given as

follows. When �m=�c is small, it is more likely to find theUE in the last interacted cell. In this case, dynamic pag-ing selects the CTT scheme to search the UE, and boththe dynamic and CTT pagings have similar and good per-formance (in Figure 6, the values of the ı and � curvesare close to 1). On the other hand, when �m=�c is large,the dynamic paging is more likely to select the TT or the3G scheme. In this case, if p is small, we observe that thedynamic paging likely selects the TT scheme, which has aslightly lower paging cost than the CTT scheme [8]. There-fore, the dynamic paging outperforms the CTT paging (inFigure 6(a), the values of the ˘ curve are smaller than 1).On the other hand, if p is large, because of the high pag-ing cost of the 3G scheme, the paging cost of the dynamicscheme is slightly higher than that of the CTT scheme (inFigure 6(b), the values of the ˘ curve are slightly largerthan 1). We note that the performance discrepancies of thepaging cost between the dynamic and the CTT pagings arewithin 0:2% for all input parameter setups under our study.

5. CONCLUSIONS

This paper proposed the dynamic paging scheme for LTEmobility management. The performance is measured bythe expected number Cd;s of polling cycles before the UEis found and the expected numberCp;s of paged cells whenan incoming call arrives. We compare the performance ofthe dynamic paging with the best static paging schemecalled CTT. Our study indicates the following results:

� For the Cd;s performance, when V is small and�m=�c is large (i.e., movement pattern is regu-lar and the UE moves frequently), the dynamicpaging outperforms the CTT paging. On the otherhand, when V is large or �m=�c is small, the



dynamic paging and the CTT paging have similarperformance.

� For the Cp;s performance, the dynamic and CTTschemes have similar performance for all inputparameter setups under our study.

In summary, the dynamic paging scheme is better than theCTT paging scheme.

APPENDIX A: DETAILEDSIMULATION PROCEDURES

This appendix describes the detailed simulation proce-dures for the dynamic and CTT schemes. A clock t ismaintained to indicate the simulation progress, which isthe timestamp of the event being processed. All eventsare inserted into the event list and are deleted/processedfrom the event list in the non-decreasing timestamporder. An array I Œi � is maintained to record the sce-nario type of the i th incoming call (e.g., I Œi � D 1

means that the UE resides in the last interacted cell whenthe i th call arrives). Figure A.1 illustrates the simula-tion flow chart for the dynamic paging scheme with thefollowing steps:

Step 1. Set the counters (i.e., i , nd , and np) andthe simulation clock t to 0. Initialize Nx, Ny, x�,and y� by randomly selecting integers from 1 topNCNT .

Step 2. The first Call event e1 and Move event e2 are gen-erated. For event e1, e1:type is Call, and e1:ts Dt C tc where tc is generated from GC . For event e2,e2:type is Move, and e2:ts D t C tm where tm isgenerated from GM . Events e1 and e2 are insertedinto the event list.

Steps 3 and 4. The first event e in the event list is deletedand processed on the basis of its type. The simulationclock t is set to e:ts. If e:type is Call, Step 5 is exe-cuted. If e:type is Move, the simulation proceeds toStep 20.

Steps 5–17 simulate a Call event, which are described asfollows.

Step 5. When an incoming call arrives, i is incrementedby one.

Step 6. As mentioned in Section 2, if i = 1, we do not haveany history datum to estimate the paging cost of eachpaging scheme. In this case, we select the 3G schemebecause the 3G scheme has the smallest paging delay,and Step 15 is executed. Otherwise, the flow goes toStep 7.

Step 7. The MME computes nI .i/ based on I Œj � wherei �m� � j � i � 1, and for s 2 fCT T ; T T ; 3Gg,Cp;s.i/ are calculated from nI .i/ and equations(1)–(3).

Step 8. As mentioned in Section 2, the MME selects thepaging scheme s with the smallest Cp;s.i/. If two or

more schemes have the smallestCp;s.i/, the one withthe smallest Np is selected.

Step 9. If s D CT T , Step 10 is executed. If s D T T , thesimulation proceeds to Step 13. If s D 3G, the flowgoes to Step 15.

Steps 10 and 11 (CTT is exercised). The MME sends thepaging message to the last interacted cell, and bothnd and np are incremented by one. If the UE residesin the last interacted cell (i.e., x� D Nx and y� D Ny),then the UE will receive the paging message, and thesimulation proceeds to Step 16. Otherwise, Step 12 isexecuted.

Step 12. If a TA only contains one cell (i.e., NC D 1), theTA of the last interacted cell has paged the UE in Step10, and the UE is not found in Step 11. In this case,Step 15 is executed to search the UE in all cells of theTAL. Otherwise, the flow goes to Step 13.

Steps 13 and 14 (TT is exercised). The MME sends thepaging messages to the TA of the last interacted cell.Therefore, np is incremented byNC , and nd is incre-mented by one. If the UE resides in the TA of thelast interacted cell (i.e.,

˙x�=pNC

�D˙Nx=pNC

�and

˙y�=pNC

�D˙Ny=pNC

�), the UE is found,

and Step 16 is executed. Otherwise, the simulationproceeds to Step 15.

Step 15 (3G paging is exercised). The MME sends thepaging messages to all cells in the TAL. Therefore,np is incremented by NCNT , and nd is incrementedby one.

Step 16. The MME records the scenario type I Œi � of thei th incoming call as follows:

if x� D Nx and y� D Ny then I Œi � 1;

else if˙x�=pNC

�D˙Nx=pNC

�and˙

y�=pNC

�D˙Ny=pNC

�then I Œi � 2;

else I Œi � 3.

Then, the MME updates the last interacted cell bysetting h Nx; Nyi to hx�; y�i.

Step 17. The next Call event e1 is generated and insertedinto the event list, where e1:ts D t C tc .

Step 18. If 10 million of Call events have been processed,Step 19 is executed. Otherwise, Step 3 is executed. Inour experience, 10 million of Call events are enoughto produce stable statistics.

Step 19. The performance measures are computed by (4),and the simulation terminates.

Steps 20–24 handle a Move event, which are described asfollows.

Step 20. When the UE crosses the cell boundary to aneighboring cell, the movement direction is deter-mined by the uniform random number U generatedby GD . From Figure 2, new hx�; y�i are updated bythe following routing rules:



Figure A.1. Simulation flow chart for the dynamic paging scheme.

hx�; y�i

8̂̂ˆ̂̂̂ˆ̂̂̂̂ˆ̂̂̂ˆ̂̂̂̂<̂ˆ̂̂̂ˆ̂̂̂̂ˆ̂̂̂ˆ̂̂̂̂ˆ̂̂:

hx� � 1; y�C 1i; for 0� U <1� 3p

5

hx� � 1; y�i; for1� 3p

5� U <

2.1� 3p/

5

hx� � 1; y� � 1i; for2.1� 3p/

5� U <

3.1� 3p/

5

hx�; y�C 1i; for3.1� 3p/

5� U <

4.1� 3p/

5

hx�; y� � 1i; for4.1� 3p/

5� U < 1� 3p

hx�C 1; y�C 1i; for 1� 3p � U < 1� 2p

hx�C 1; y�i; for 1� 2p � U < 1� p

hx�C 1; y� � 1i; for 1� p � U � 1

(A.1)



Step 21. If the UE leaves the current TAL (i.e., x� D 0 orpNCNT C 1, or y� D 0 or

pNCNT C 1), Step 22 is

executed. Otherwise, Step 24 is executed.Step 22. As mentioned before, when the UE leaves the cur-

rent TAL, the entrance cell is reset to the cell in thecentral TA. Therefore, x� and y� are set as

x� pNC

��pNT

2

��

�x�pNC

��C x� (A.2)

and

y� pNC

��pNT

2

��

�y�pNC

��C y� (A.3)

Step 23. The MME updates the last interacted cell bysetting h Nx; Nyi to hx�; y�i.

Step 24. The next Move event e2 is generated and insertedinto the event list, where e2:ts D tCtm. The simulationjumps to Step 3.

The simulation flow chart for the CTT scheme is sim-ilar to that in Figure A.1 except that Steps 6–9 and thearray I Œi � in Step 16 are not needed in the CTT simu-lation. Moreover, after the execution of Step 5, the CTTsimulation goes to Step 10.

APPENDIX B: NOTATION

The notation used in this paper is listed in the succeedingtext.

� p: the probability that the UE moves to one of theupper-right, right, and lower-right neighboring cells.

� hx; yi: the label of an arbitrary cell in a TAL(x: column label; y: row label).

� h Nx; Nyi: the label of the last interacted cell ( Nx: columnlabel; Ny: row label).

� hx�; y�i: the label of the cell where the UE currentlyresides (x�: column label; y�: row label).

� hX; Y i: the label of an arbitrary TA in a TAL(X : column label; Y : row label).

� Cd;s : the expected number of polling cycles beforethe UE is found for the dynamic paging .s DD/ andthe CTT paging .s D CT T /, respectively.

� Cp;s : the expected number of paged cells when anincoming call arrives for the dynamic paging .s DD/and the CTT paging .s D CT T /, respectively.

� Cp;s.i/: the average number of paged cells for the sscheme between the .i � m�/th call arrival and the.i � 1/th call arrival, where s 2 fCT T ; T T ; 3Gg.

� t : the simulation clock.� tc : the inter-call arrival time.� tm: the cell residence time.� 1=�c DEŒtc �: the mean inter-call arrival time.� 1=�m DEŒtm�: the mean cell residence time.� V : the variance for the tm distribution.

� m: the number of the most recent incoming callarrivals.

� m�: the smaller of i � 1 and m.� NC : the number of cells in a TA.� NT : the number of TAs in a TAL.� Np : the maximum number of polling cycles before

the UE is found.� nI .i/: the number of scenarios I occurred between

the .i�m�/th call arrival and the .i�1/th call arrivalwhere I 2 f1; 2; 3g.

� i : the number of incoming calls.� nd : the number of polling cycles.� np : the number of paged cells.� GC : the exponential random number generator.� GM : the Gamma random number generator.� GD : the uniform random number generator.� e, e1, e2: the events in the simulation.� U : the uniform random number drawn from GD .� I Œi �: the scenario type of the i th incoming call arrival.� s: the paging scheme (s D D for dynamic paging,s D CT T for Cell-TA-TAL paging, s D T T forTA-TAL paging, and s D 3G for third generationpaging).

ACKNOWLEDGEMENTS

Y.-B. Lin’s work was supported in part by the NSC100-2221-E-009-070 and 101-2221-E-009-032, AcademiaSinica AS-102-TP-A06, Chunghwa Telecom, IBM, ArcadyanTechnology Corporation, the ITRI/NCTU JRC ResearchProject, the ICL/ITRI Project, Nokia Siemens Networks,Department of Industrial Technology (DoIT) AcademicTechnology Development Program 100-EC-17-A-03-S1-193, and the MoE ATU plan. R.-H. Liou’s work wassupported by the MediaTek Fellowship.

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AUTHORS’ BIOGRAPHIES

Yi-Bing Lin is the vice president andlife chair professor of the Collegeof Computer Science, National ChiaoTung University (NCTU) and a visit-ing professor of King Saud University.He is also with the Institute of Informa-tion Science and the Research Centerfor Information Technology Innova-

tion, Academia Sinica, Nankang, Taipei, Taiwan. Lin is theauthor of the books Wireless and Mobile Network Archi-tecture (Wiley, 2001), Wireless and Mobile All-IP Net-works (John Wiley, 2005), and Charging for Mobile All-IPTelecommunications (Wiley, 2008). Lin received numer-ous research awards including the 2005 NSC DistinguishedResearcher and the 2006 Academic Award of Ministry ofEducation. Lin is a fellow of ACM, AAAS, IEEE, and IET.

Ren-Huang Liou received his BS andMS degrees in Computer Science fromthe National Chiao Tung University(NCTU), Hsinchu, Taiwan, in 2007and 2009, respectively. He is currentlyworking toward his PhD degree atNCTU. His current research interestsinclude Voice over Internet Protocol

(VoIP), mobile computing, and performance modeling.

Chun-Ting Chang received his BSdegree in Computer Science fromthe National Chiao Tung University(NCTU), Hsinchu, Taiwan, in 2012.She is currently working toward her MSdegree at NCTU. Her current researchinterests include design and analysis ofpersonal communications services net-

work and mobile augmented reality.


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